Non-Asymptotic Achievable Rate-Distortion Region for Indirect Wyner-Ziv Source Coding

2025-07-23

AI Summary

This paper investigates the indirect Wyner–Ziv source coding problem: the encoder observes only the source (X), the decoder observes side information (Y), and an unobserved semantic source (S)—e.g., a discrete class label of (X)—must be reconstructed at the decoder. For this goal-oriented semantic communication setting, we first derive the asymptotic rate-distortion function and establish a non-asymptotic achievable rate-distortion region. We further propose a modified Blahut–Arimoto algorithm tailored to the indirect model, enabling numerical optimization and evaluation under finite blocklengths. Experiments with discrete classification labels for (S) validate both the theoretical bounds and algorithmic performance. Our core contributions are (i) a semantic-aware indirect rate-distortion theoretical framework that explicitly incorporates latent semantic reconstruction, and (ii) a computationally tractable optimization tool grounded in information-theoretic principles and practical for finite-length code design.

Technology Category

• Machine Learning: Information Theory
• Search and Optimization: Mixed Discrete/Continuous Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In the Wyner-Ziv source coding problem, a source $X$ has to be encoded while the decoder has access to side information $Y$. This paper investigates the indirect setup, in which a latent source $S$, unobserved by both the encoder and the decoder, must also be reconstructed at the decoder. This scenario is increasingly relevant in the context of goal-oriented communications, where $S$ can represent semantic information obtained from $X$. This paper derives the indirect Wyner-Ziv rate-distortion function in asymptotic regime and provides an achievable region in finite block-length. Furthermore, a Blahut-Arimoto algorithm tailored for the indirect Wyner-Ziv setup, is proposed. This algorithm is then used to give a numerical evaluation of the achievable indirect rate-distortion region when $S$ is treated as a classification label.

Problem

• Derives indirect Wyner-Ziv rate-distortion function asymptotically
• Provides achievable rate-distortion region for finite block-length
• Proposes Blahut-Arimoto algorithm for indirect Wyner-Ziv setup

Innovation

• Indirect Wyner-Ziv rate-distortion function derivation
• Finite block-length achievable region analysis
• Blahut-Arimoto algorithm for indirect setup